Ionization of metal clusters by ions in the Fermi velocity range

We simulate excitation of metal clusters by highly charged, energetic ions, analyzing electron emission in terms of discrete ionization probabilities. Our test case is the collision of on the cluster at velocities around the electronic Fermi velocity of bulk sodium. The calculations are performed with a density-functional approach, using the time-dependent local density approximation. We find that ionization takes place on an extremely short time scale of less than 5 fs. The preferred final charge state depends sensitively on the impact parameter. High ionization can easily be achieved in sufficiently close collisions. Direct trapping through the by-passing ion is found to be of little importance at the velocities considered. Received: 28 July 1997 / Received in final form: 23 December 1997 / Accepted: 8 January 1998     

Towards spectral pattern of spin polarized sodium clusters: The example of Na

We investigate spin modes in the ground state and the polarized first isomer of the Na₁₂ cluster describing the valence electrons in time-dependent local-spin-density approximation (TDLSDA) and the detailed ionic background using local pseudopotentials. The spin modes show a collective redshift compared to the unperturbed particle-hole excitations. They are strongly fragmented and the average energy of the modes along the principal axes are related to the underlying geometry (triaxial or axially symmetric). For the polarized isomer, we find significant cross talk between the spin modes and the dipole plasmon, which hints at a possible spectroscopic identification. Received: 22 June 1998 / Accepted: 29 July 1998     

Geometrical and quantal fragmentation of optical response in

By comparing quantal and semi-classical calculations of optical response, we work out the part of the splitting of the plasmon spectra which is exclusively due to geometrical effects. We apply the analysis to the test case which exhibits an interesting geometry with strong prolate quadrupole deformation and a pronounced asymmetry in addition. We find a new type of resonance splitting which is due to geometrical effects but goes beyond the simple and well known deformation splitting. Received: 6 April 1998 / Accepted: 24 April 1998     

Hindered Coulomb explosion of embedded Na clusters — stopping,shape dynamics and energy transport

We investigate the dynamical evolution of a Na₈ cluster embedded in Ar matrices of various sizes from N=30 to 1048. The system is excited by an intense short laser pulse leading to high ionization stages.We analyze the subsequent highly non-linear motion of cluster and Ar environment in terms of trajectories, shapes, and energy flow. The most prominent effects are: temporary stabilization of high charge states for several ps, sudden stopping of the Coulomb explosion of the embedded Na₈ clusters associated with an extremely fast energy transfer to the Ar matrix, fast distribution of energy throughout the Ar layers by a sound wave. Other ionic-atomic transfer and relaxation processes proceed at slower scale of few ps. The electron cloud is almost thermally decoupled from ions and thermalizes far beyond the ps scale.     

Landau fragmentation and deformation effects in dipoSe response of sodium clusters

Recent experimental data on the dipole plasmon in axial sodium clusters Na _N ⁺ with 11 ≤ N ≤ 57 are analyzed within a self-consistent separable random-phase approximation (SRPA) based on the deformed Konh-Sham functional. Good agreement with the data is achieved. The calculations show that, while in light clusters plasmon properties (gross structure and width) are determined mainly by deformation splitting, in medium clusters with N τ 50 the Landau fragmentation becomes decisive. Moreover, in medium clusters shape isomers come to play with contributions to the plasmon comparable with the ground state one. As a result, commonly used methods of the experimental analysis of cluster deformation become useless and correct treatment of cluster shape requires microscopic calculations.     

Nanoplasma dynamics in Xe clusters driven by ultraintense laser fields

We present a theoretical and computational study of the properties and the response of the nanoplasma and of outer ionization in Xe_n clusters (n = 55–2171, initial cluster radius R₀ = 8.7–31.0 ?) driven by ultraintense near-infrared laser fields (peak intensity I_M = 10¹⁵–10²⁰ Wcm^-2, temporal pulse length τ= 10–100 fs, and frequency ν= 0.35 fs^-1). The positively charged high-energy nanoplasma produced by inner ionization nearly follows the oscillations of the fs laser pulse and can either be persistent (at lower intensities of I_M = 10¹⁵–10¹⁶ Wcm^-2 and/or for larger cluster sizes, where the electron energy distribution is nearly thermal) or transient (at higher intensities of I_M = 10¹⁸–10²⁰ Wcm^-2 and/or for smaller cluster sizes). The nanoplasma is depleted by outer ionization that was semiquantitatively described by the cluster barrier suppression electrostatic model, which accounts for the cluster size, laser intensity and pulse length dependence of the outer ionization yield. The electrostatic model was further utilized for estimates of the laser intensity and pulse width dependence of the border radius R₀ ^(I) for the attainment of complete outer ionization at , while at R₀ > R₀ ^(I) a persistent nanoplasma prevails. R₀ ^(I) establishes an interrelationship between electron dynamics and nuclear Coulomb explosion dynamics in ultraintense laser-cluster interactions.     

Ionic recoil energies in the Coulomb explosion of metal clusters

The photoionization of metal clusters in intense femtosecond laser fields has been studied. In contrast to an experiment on atoms, the interaction in this case leads to a very efficient and high charging of the particle where tens of electrons per atom are ejected from the cluster. The recoil energy distribution of the atomic fragment ions was measured which in the case of lead clusters exceeds 180 keV. Enhanced charging efficiency which we observed earlier for specific pulse conditions is not reflected in the recoil energy spectra. Both the average and the maximum energies decrease with increasing laser pulse width. This is in good agreement with molecular dynamics calculations. Received 20 December 2000     

Trianionic gold clusters

Using Penning-trap experiments and a shell-correction method incorporating ellipsoidal shape deformations, we investigate the formation and stability patterns of trianionic gold clusters. Theory and experiment are in remarkable agreement concerning appearance sizes and electronic shell effects. In contrast to multiply cationic clusters, decay of the trianionic gold clusters occurs primarily via electron autodetachment and tunneling through a Coulomb barrier, rather than via fission. Received 9 January 2001     

Photoionization of argon, krypton and xenon clusters in the inner valence shell region

Photoionization of rare gas clusters in the innervalence shell region has been investigated using threshold photoelectron and photoion spectrometers and synchrotron radiation. Two classes of states are found to play an important role: (A) valence states, correlated to dissociation limits involving an ion with a hole in its innervalence ns shell, (B) Rydberg states correlated to dissociation limits involving an ion with a hole in its outervalence np shell plus an excited neutral atom. In dimers, class A states are “bright”, that is, accessible by photoionization, and serve as an entrance step to form the class B “dark” states; this character fades as the size of the cluster increases. In the dimer, the “Mulliken” valence state is found to present a shallow potential well housing a few vibrational levels; it is predissociated by the class B Rydberg states. During the predissociation a remarkable energy transfer process is observed from the excited ion that loses its innershell electron to its neutral partner. Received: 10 February 1998 / Revised: 17 July 1998 / Accepted: 31 July 1998     

The effect of volumetric weighting in the interaction of intense laser fields with clusters

Silver clusters embedded in helium nanodroplets are exposed to intense femtosecond laser pulses (10¹³ - 10¹⁶ W/cm²). The signal of highly charged (q≤11) atomic fragments is maximized by delayed plasmon enhanced ionization using stretched laser pulses. Further details with respect to the dynamics of the charging process can be obtained, when the intensity distribution within the laser focus is taken into account. For the first time, the z-scan method is applied to clusters which offers a route to investigate the explicit dependence of the ion signals with respect to the laser intensity. By taking advantage of the volumetric weighting effect ionization thresholds are determined, yielding values well below 10¹⁴ W/cm² for Ag^q+ ions with q≤11.     

Electronic structure and magnetism in 4d-transition metal clusters

We analyze the stability of magnetic states obtained within the tight-binding model for cubooctahedral (O_h) and icosahedral (I_h) clusters of early 4d (Y, Zr, Nb, Mo, and Tc) transition metals. Several metastable magnetic clusters are identified which suggests the existence of multiple magnetic solutions in realistic systems. A bulk-like parabolic behavior is observed for the binding energy of O_h and I_h clusters as a function of the atomic number along the 4 d-series. The charge transfer on the central atom changes sign, while the average magnetic moments present an oscillatory behavior as a function of the number of d electrons in the cluster. Our results are in agreement with other theoretical calculations. Received: 20 November 1997 / Received in final form: 9 March 1998 / Accepted: 30 March 1998     

Stability and fragmentation of multiply ionized clusters

The stability of neutral, singly and multiply ionized silicon clusters, (N = 2-7, M = 0, , , ), has been investigated using an ab initio density functional method. We show that the fragmentation effect significantly affects the structure of mass-spectra of multiply ionized silicon clusters. For clusters, the clusters with a large fragmentation energy are found to correspond to the high peaks at N = 4 and 6 in mass-spectra. For clusters, a peak at N = 5 in mass-spectra has been predicted to be especially high. Received: 9 June 1997 / Revised: 8 January 1998 / Accepted: 25 February 1998     

Simulation of small positively charged MgO clusters and study of their electronic densities

With the help of ab initio methods the clusters [(MgO)₁₃Mg] ^Q+ are simulated for Q = 0, 1, 2. Then, vacancy clusters [(MgO)₁₂Mg₂] ^Q+ obtained by removing one oxygen atom are computed for Q running from 0 to 4. These clusters exhibit a slight sphericity and generally shorter interatomic distances than in the crystal. The electronic densities variations are studied in function of Q. In particular, it is observed that the electronic density in the oxygen vacancy goes to a maximum when Q = 2. The ionisation potentials vary from approximately 4 to 14 eV when Q varies from 0 to 3, with a more rapid increase from Q = 1 to Q = 2. The stability study of vacancy clusters show that they experience a phase transition when their charge becomes equal to 2, in accordance with the features mentioned above. Received 14 September 1999 and Received in final form 2 December 1999     

Interpretive approach to collective effects of electrons in multicenter problems

Interpretive theoretical tools prove valuable in guiding the analysis of experiments in the realm of atomic clusters. Here, we review basic elements of an analytic approach that makes it possible to find and visualize the effective electrostatic potential and Coulomb correlations in multicenter problems. To illustrate the utility of these concepts we apply them to exploring molecular-doped metallic clusters. This study is aiming at a systematic, visual assessment of changes induced in screening, Coulomb correlation and effective potential by varying the charge of the electronegative impurity and its position in the cluster cage.     

Temperature-dependent ionization potential of sodium clusters

The ionization potential of sodium clusters () at a finite temperature is studied using density functional theory and ab initio molecular dynamics. The threshold regions of the photoionization efficiency curves are deduced from the integrated IP distributions, which are obtained from the energy eigenvalues of the highest occupied Kohn-Sham states during molecular dynamics by applying a theoretically well-defined shift. The calculated ionization potentials are directly compared to the experimental values. The energetically best geometry of Na₅₅ is found to be a slightly distorted icosahedron. Received 16 April 1999 and Received in final form 6 July 1999     

Electronic state of gold in supported clusters

The electronic states of gold in gold supported nanoparticles modified by Ce, Zr, La and Cs oxides have been studied by the methods of IR spectroscopy of adsorbed CO, UV-visible spectroscopy of diffuse reflectance, XRD and electron microscopy. The additives of Ce and Zr oxides stabilize the ionic states of supported gold and increase the effective charge of the ions. In contrast, La and Cs oxides lower the ion effective charge and favour their fast reduction under redox treatments and reaction medium. It is explained by electron donor-acceptor interaction of the supported metal nanoparticles with the modifiers.     

The influence of O and C doping on the ionization potentials of Li-clusters

The influence of doping of Li-clusters by electronegative O and C atoms on the ionization potentials was investigated. Experimentally, we report ionization potentials for bare Li_n clusters deduced from photoionization efficiency spectra. The values are compared with the results for Li_nO and Li_nC clusters. Observed differences are largely attributed to a quantum size effect caused by the segregated molecular part around the impurity, which changes the electron work function. Theoretically, the Fermi and exchange-correlation energies which enter the work function, are calculated in the frame of the augmented plane wave (APW) method by taking explicitly into account the presence of the molecular core. The other contribution to the work function, the moment of the double layer at the cluster surface, is computed by solving the corresponding Poisson's equation. Received 9 September 1999 and Received in final form 7 February 2000     

Effect of melting on ionization potential of sodium clusters

The effect of melting transition on the ionization potential has been studied for sodium clusters with 40, 55, 142, and 147 atoms, using ab initio and classical molecular dynamics. Classical and ab initio simulations were performed to determine the ionization potential of Na₁₄₂ and Na₁₄₇ for solid, partly melted, and liquid structures. The results reveal no correlation between the vertical ionization potential and the degree of surface disorder, melting, or the total energy of the cluster obtained with the ab initio method. However, in the case of 40 and 55 atom clusters, the ionization potential seems to decrease when the cluster melts. Received 1st November 2002 Published online 24 April 2003 RID="a" ID="a"e-mail: ar@phys.jyu.fi     

Doubly charged clusters - neutral atom charge transfer: the role of the Coulombic repulsion

We have studied experimentally the collisional charge transfer between a neutral atom and a multicharged metal-atom cluster. The charge transfer cross section measured for Na ₃₁ ^{+ +} + Cs is in the range of 400 ?². The time-of-flight mass analysis of the singly charged collision products demonstrates that an energy of about 0.5 eV is deposited in the cluster fragment during the charge transfer collision. This effect can be interpreted as a charge transfer to an excited state of the metal cluster. The measured cross section for Na ₃₁ ^{+ +} + Cs is larger than the one for Na ₃₁ ⁺ + Cs collisions. This difference between these two systems is due to the existence, for the first one, of a Coulombic repulsion term in the collision output channel. Received 24 October 2000